Beyond the first main theorem – when is the solution of a linear cauchy problem computable?

Authors:
Klaus Weihrauch;Ning Zhong
Affiliations:
University of Hagen, Hagen, Germany;University of Cincinnati, Cincinnati, OH
Venue:
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Year:
2006

Citing 3
Cited 0

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Abstract

We study computabilty of the abstract linear Cauchy problem du(t)/dt=Au(t), t0, u(0)=x∈X where A is a linear operator on a Banach space X. We give necessary and sufficient conditions for A such that the operator K:x↦ u is computable. We consider continuous operators and more generally closed operators A. For studying computability we use the representation approach to Computable Analysis (TTE) [7, 1] which is consistent with the model used in [6].